How do I force a refresh after rendering animation?
You don't need to refresh anything, lighting is always up to date and recalculated per render, unless you somehow baked it into the objects.

How are you rendering this, using Cycles? Could you post some screenshots or perhaps a blender file?

Hemi lights are not supported in Cycles, they will render as point lights as stated in the Blender Manual, and in most situations you will want only one sun light in your scene, so perhaps use some area lights instead, and use the world background for ambient light.

Edit

You scene is updating real time as expected, see bellow.



Deleting lights updates the scene immediately

Some random tips

Hemi lights are like ambient lights, they emit light from a 180º dome, you generally do not want many of them in your scene. Many will cause a washed out and bland lighting that will absorb details.

Also sun lights are generally used sparingly in most scenes because they emit parallel rays of light. Try using a mix of spot lights, point lights and area lamps instead.

Edit II
Disable Compositing and Sequencer in the Properties Window > Render > Post Processing